In the figure given below, lines $PQ$ and $RS$ are parallel. For what value of $x$ will the lines $AB$ and $CD$ be parallel?

In the figure given below, $AB\parallel CD$ and $EF\parallel DQ$. Determine $\angle AED, \angle DEF$ and $\angle PDQ$.

In the figure given below, $AB\parallel CD$. Find the value of $x$.

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.

In the figure given below, bisectors $AP$ and $BQ$ of the alternate interior angles are parallel. Show that lines $m$ and $n$ are parallel.

In the figure given below, $AB\parallel DE$. Show that $\angle x+\angle y-\angle z=180°$.

Can a triangle have all angles less than $60°$? Give a reason for your answer.

Can a triangle have two right angles? Give a reason for your answer.

Can a triangle have two right angles? Give a reason for your answer.